In unsupervised learning, what is meant by "finding the probability of an image"?
When you say likelihood, you are invoking several other concepts like events, sample, parameters, model, probability density function (PDF), etc (it would be helpful if you learn more about these concepts). In essence, a likelihood function $l(x|\theta)$ is a PDF that quantifies how likely is that event $x$ happens out of a set of possible events, given the parameters $\theta$ that define your model.  

In the specific case of images, the set of possible events is usually one of two options: 1) all the available images in a dataset, or 2) all the existing images. Usually you want to model the likelihood in the option 2), but only having access to a sample of all the possible images. In either case, the likelihood is just the probability that you select one image out of all the possible ones. If you consider only images of $1048\times 720$ pixels, the possible amount of images is $(256\times3)^{1048\times 720}$, where I am assuming that each pixel consists of 3 colors and each color can take 256 values. Since the amount of possible images is so so big, it is very common that the probability of selecting a specific one is very very small. This is a reason why you usually work with log-likelihood (the logarithm of the likelihood) instead of directly using likelihoods. For example, if all your images were equally probable, the likelihood would be in the order of $10^{-{10^7}}$, while the log-likelihood would be around $-10^7$.  

To solve your paradox with the probability of images and pixels, consider that instead of pixels you have coins and instead of images you have sequences of coins. Let's say that you have a fair coin, so the probability of tails ($T$) after tossing the coin is 0.5. If you toss a second coin, the probability of having $T$ again is naturally 0.5 as well, but what is the probability that both results where $T$? It is the product (0.25) since the events are independent. Similarly, the probability of the other three sequences $TH$, $HT$ and $HH$ is just 0.25. You can see that since the probability needs to be shared between 4 sequences equally probable, they are less probable with respect to the probabilities of the sequences of length 1. If you toss the coin 3 times, then the probability of all these coins being tails is just $0.5^{3}$. Again, there are now 8 possible sequences, all sharing the same amount of probability. You can see what's going on. Since the amount of possible options becomes large, the probability of each possible sequence of coins becomes small. Clearly, you would never toss a coin 10 times and expect to obtain all $T$, right? Well, exactly the same happens in the case of the pictures.